The Arcology Tokens can be traded in at the faction vendor "Sloane" in Siren's Watch region. The Arcology Tokens will increase the reputation with Sloane. Each reputation level takes 20 Arcology Tokens and rewards you with one random purple engram from the vendor's pool of items.
In other words: every 20 Arcology Tokens give you one engram with 1-2 legendary (purple) gear pieces. More tokens can be earned from completing public events, looting random chests and defeating high value targets.

This is a very quick and easy way to get good gear, especially after hitting level 20. It only takes 4 minutes to collect all 6 chests when following this video guide and you can earn 2 legendary items from it! That's one of the fastest ways to improve your gear in Destiny 2.